After the magnitude of what happened at Liverpool's Anglican cathedral 11 days earlier, obliterating 23 years of scandalous untruth about football's most dreadful disaster, this was a grey, chilly afternoon at Anfield where the game itself struggled to match up.

The efforts before Liverpool's match against Manchester United, the expressions of togetherness, the tributes to the bereaved Hillsborough families, and their battle for justice, were consummately realised. But hopes for similar grandeur in the sporting contest rather shrank; Jonjo Shelvey's sending off for lunging in on 39 minutes changed the match into a bad-tempered patchwork, ultimately decided in United's favour by a 81st-minute penalty which the Liverpool crowd, and the manager Brendan Rodgers, vehemently disputed.

Some United fans kept behind after the match were, sadly, heard singing their songs about "murderers" and "victims", taken as a slur about Hillsborough. According to reports they were responding to a couple of Liverpool supporters making aeroplane gestures as a taunt about the Munich air crash. That dismal exchange happened in an otherwise empty ground, however, and during a fractious game supporters were tetchy rather than hostile.

Football never was more important than life and death, of course; Bill Shankly meant that as a quotable quip about the British passion for it, before the horrors of Bradford, Heysel and Hillsborough cast the remark in a dark perspective. The truth around his bon mot is that football often falls short, as it did for years after Hillsborough, when actually confronted by matters of life and death. After the apologies, from Sheffield Wednesday then the Football Association, finally and belatedly rolled in with the Hillsborough Independent Panel's conclusive report, bereaved, vindicated families asked angrily where they had been for 23 years.

Before the game which brought this bitter rivalry to Anfield, there was a hush in the streets outside, suggesting some emotional unity might have been forged between the clubs, too often lacking in modern football.

Crowds assembled around the memorial at the Shankly gates to the 96 Liverpool supporters who died at Hillsborough in 1989, with its two awfully long rows of names, listed in alphabetical order from John Anderson, 62, to Graham John Wright, 17. Many Liverpool supporters touched the marble, some kissed it, before they moved away.

Inside, the staged tributes were grand and well executed. Sir Bobby Charlton, his own life in football so overcast by Manchester United's tragedy at Munich, handed the Liverpool legend Ian Rush a bouquet of roses as a symbol of fraternity. Sir Alex Ferguson's landmark expression of solidarity with the Hillsborough families, applauding their campaign for justice, had been handed to all the United fans filing in through the Anfield Road turnstiles, just along from the memorial.

On the pitch, The captains Steven Gerrard and Ryan Giggs released the red balloons as planned, 48 each, to let the monstrous total of 96 float up into the clouds. The sight of card mosaics displaying the words Truth, and Justice, in the Kop and Centenary stands, while You'll Never Walk Alone was sung with a meaning weightier than a pop song ever intended, was great theatre of reconciliation.

And during the ritual handshake, Luis Suárez did shake Patrice Evra by the hand, so avoiding another flashpoint in that unworthy chapter of discord.

When the game kicked off, Liverpool supporters kept to their plan of maintaining the mosaic display: a minute for truth and justice, they called it. Then they put the cards down, roared for Liverpool, and a football match unfolded, with its high skill, imperfections and ill-temper.

Comparisons had rightly been drawn with United's derby against Manchester City in 2008, when the emotions surrounding the 50-year anniversary of Munich affected United's ability to concentrate on the game and they lost 2-1. Yet here, Liverpool seemed remarkably able to focus on the game, including Gerrard, who talked movingly in the week about losing his cousin, Jon-Paul Gilhooley, then 10, the youngest victim of Hillsborough.

Shelvey, fuming with Ferguson as he left the field, protested later that he was only competing for the ball with United's Jonny Evans, whom Rodgers claimed should have been sent off too. But Shelvey had thrown himself in dangerously, having not been booked for a reckless foul on Rafael da Silva after 15 minutes, so perhaps the emotional charge in the occasion had got to him, in the wrong way.

After all that has emerged about Hillsborough, and the unified response it prompted around football, some of the game's dismal realities reasserted themselves rather too quickly. United fans, from the start, were not particularly inclined to accept the occasion as a day to suspend hostilities for so long soured into this rivalry. As the Liverpool crowd quietened following the Hillsborough tributes, and tried to get its head around the football, some in United's corner baited them with "Where's your famous Munich song?". Liverpool's fans, for a time in the first half, booed Evra, whose complaint of racial abuse against Suárez was upheld by the FA.

Gerrard still managed to volley Liverpool ahead within the first minute of the second half, but Paul Scholes, on for Nani, graced the space from which Shelvey had been expelled, and Rafael's curled equaliser arrived just five minutes later. Television replays showed Suárez should have had a penalty before Antonio Valencia was clipped by Glen Johnson and Robin van Persie won the game for United.

Afterwards, Rodgers praised Liverpool's supporters and the pre-match tributes, saying: "People who value human decency and humanity will have been proud today, because it's important we move on from a lot of negative stuff." Ferguson agreed: "It demonstrates that two great clubs can unite and do these things, and then get on with the game of football with both teams trying to win."

This sporting occasion did begin in remembrance of one of the most remarkable campaigns for justice, against a scandalous police cover-up, but it ended largely in rancour, and complaints about a referee, Mark Halsey.

After the truth about Hillsborough broke through, it felt as if it might be a watershed for a better era in football. It still may be, but the afternoon at Anfield showed it will take time and sustained effort – more than a minute for truth and justice.